60 citations · 131 across the 21 of their papers we have counts for
6 papers · 1 filter
A bound for the error term in the Brent-McMillan algorithm
Richard P. Brent, Fredrik Johansson
The Brent-McMillan algorithm B3 (1980), when implemented with binary splitting, is the fastest known algorithm for high-precision computation of Euler's constant. However, no rigor…
Evaluating parametric holonomic sequences using rectangular splitting
Fredrik Johansson
We adapt the rectangular splitting technique of Paterson and Stockmeyer to the problem of evaluating terms in holonomic sequences that depend on a parameter. This approach allows c…
Using functional equations to enumerate 1324-avoiding permutations
Fredrik Johansson, Brian Nakamura
We consider the problem of enumerating permutations with exactly r occurrences of the pattern 1324 and derive functional equations for this general case as well as for the pattern…
Rigorous high-precision computation of the Hurwitz zeta function and its derivatives
Fredrik Johansson
We study the use of the Euler-Maclaurin formula to numerically evaluate the Hurwitz zeta function for , along with an arbitrary number of derivatives…
Ore Polynomials in Sage
Manuel Kauers, Maximilian Jaroschek, Fredrik Johansson
We present a Sage implementation of Ore algebras. The main features for the most common instances include basic arithmetic and actions; gcrd and lclm; D-finite closure properties;…
Finding Hyperexponential Solutions of Linear ODEs by Numerical Evaluation
Fredrik Johansson, Manuel Kauers, Marc Mezzarobba
We present a new algorithm for computing hyperexponential solutions of ordinary linear differential equations with polynomial coefficients. The algorithm relies on interpreting for…